A square \(ABCD\) has points \(E\) and \(F\) as its midpoints on \(AD\) and \(AB\), respectively. The square is then folded such that the vertices \(A\), \(B\), and \(D\) joined together become a new vertex of the pyramid with triangular base \(EFC\).

If the square has a side length of \(6\text{ cm}\), what is the volume of the pyramid (in \(\text{cm}^3\))?

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